Umbrella animation, cloth penetration
I have been having the same problem, and already spend some nights of the last week on this. The best solution i found was to export and import the cloth simulation as described in this link. After that i put the fabric a little bit higher so that it doesn't collide anymore.
It is the best thing i come up with, but i hope someone comes with a better solution.
How can I bake the cloth simulation into keyframed vertices or shape keyed vertices?